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Prove the trigonometric identity $\csc\left(x\right)+\cos\left(x\right)\cot\left(-x\right)=\sin\left(x\right)$

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Solution

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Final answer to the problem

true

Step-by-step Solution

How should I solve this problem?

  • Prove from LHS (left-hand side)
  • Prove from RHS (right-hand side)
  • Express everything into Sine and Cosine
  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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Start by simplifying the left side of the identity: $\csc\left(x\right)+\cos\left(x\right)\cot\left(-x\right)$

Learn how to solve proving trigonometric identities problems step by step online.

$\csc\left(x\right)-\cos\left(x\right)\cot\left(x\right)=\sin\left(x\right)$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)+cos(x)cot(-x)=sin(x). Start by simplifying the left side of the identity: \csc\left(x\right)+\cos\left(x\right)\cot\left(-x\right). Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by \cos\left(x\right).

Final answer to the problem

true

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Similar Problems Solved

Prove the identity

$tan\left(x\right)+cot\left(x\right)=sec\left(x\right)cosec\left(x\right)$

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Prove the identity

$sec\left(x\right)-tan\left(x\right)sin\left(x\right)=\frac{1}{sec\left(x\right)}$

Prove the identity

$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

Prove the identity

$\tan\left(a\right)+\cot\left(a\right)=\sec\left(a\right)\csc\left(a\right)$

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$\sec x-\sin x\tan x=\cos x$

Prove the identity

$\frac{1-sin\left(x\right)}{cos\left(x\right)}=\frac{cos\left(x\right)}{1+sin\left(x\right)}$

Main Topic: Proving Trigonometric Identities

To prove a trigonometric identity, you have to show that one side of the equation can be transformed into the other side.

Used Formulas

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